Threat assessment method for air defense of warship based on variable weights intuitionistic fuzzy TOPSIS

doi:10.23919/JSEE.2026.000151

Abstract

Abstract:

Threat assessment is vital for air defense of warship, as it significantly improves decision making. Aiming at the problem that the uncertainty and combat intention of the target is not considered in the process of threat assessment for air defense of warship, a threat assessment method based on the variable weights intuitionistic fuzzy technique for order preference by similarity to ideal solution (TOPSIS) is proposed. Considering the inherent attributes and spatial situation of air targets, the threat assessment index system is established. Aiming at the uncertainty problem in the process of threat assessment, the method of transforming indexes into intuitionistic fuzzy sets (IFSs) is proposed. The objective weights and subjective weights are calculated based on intuitionistic fuzzy entropy (IFE) and combat intention, respectively. By minimizing the distance to the objectivity and subjectivity simultaneously, the calculation method of comprehensive variable weights based on the least square is proposed. An example show that the proposed method can give accurate threat degree and ranking of targets. Compared with other algorithms, it is shown that the proposed method can fully exploit the influence of the inherent attributes and spatial situation and give more reasonable results according to the target combat intention.

Key words: combat intention, air defense, threat assessment, intuitionistic fuzzy set

Wei Wu, Wenhao Bi, Mengqi Zhang, An Zhang. Threat assessment method for air defense of warship based on variable weights intuitionistic fuzzy TOPSIS[J]. Journal of Systems Engineering and Electronics, 2026, 37(4): 1225-1240.

Figures/Tables 18

Fig 1

Fig 2

Fig 3

Table 1

Table 2

Table 3

Table 4

Table 5

Table 6

IFSs of the target inherent attribute indexes"

Target	Combat capability	Type	Maneuvering capability	RCS
M1	$\left\langle {{\text{0}}{\text{.531,0}}{\text{.210}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.545,0}}{\text{.304}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.643,0}}{\text{.192}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.737,0}}{\text{.141}}} \right\rangle $
M2	$\left\langle {{\text{0}}{\text{.262,0}}{\text{.480}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.576, 0}}{\text{.245}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.4,0}}{\text{.4}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.643,0}}{\text{.192}}} \right\rangle $
M3	$\left\langle {{\text{0}}{\text{.653,0}}{\text{.089}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.789,0}}{\text{.107}}} \right\rangle $	$\left\langle {{\text{1}}{\text{.0,0}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.85,0}}} \right\rangle $
M4	$\left\langle {{\text{0}}{\text{.741,0}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.890,0}}{\text{.055}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.643,0}}{\text{.192}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.549,0}}{\text{.300}}} \right\rangle $
M5	$\left\langle {{\text{0}}{\text{.311,0}}{\text{.430}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.211,0}}{\text{.681}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.736,0}}{\text{.141}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.119,0}}{\text{.730}}} \right\rangle $
M6	$\left\langle {{\text{0}}{\text{.256,0}}{\text{.486}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.211,0}}{\text{.681}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.256,0}}{\text{.609}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.106,0}}{\text{.744}}} \right\rangle $
M7	$\left\langle {{\text{0}}{\text{.512,0}}{\text{.230}}} \right\rangle $	$\left\langle {{\text{1}}{\text{.0,0}}} \right\rangle $	$\left\langle {0.4{\text{,}}0.4} \right\rangle $	$\left\langle {{\text{0}}{\text{.650,0}}{\text{.200}}} \right\rangle $
M8	$\left\langle {{\text{0}}{\text{.641,0}}{\text{.100}}} \right\rangle $	$\left\langle {{\text{1}}{\text{.0,0}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.326,0}}{\text{.508}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.468,0}}{\text{.382}}} \right\rangle $

Table 6

Table 7

IFSs of the target inherent attribute indexes IFSs of the target spatial situation indexes at ${{\boldsymbol{t}}_{\boldsymbol{0}}}$ and ${{\boldsymbol{t}}_{\boldsymbol{1}}}$"

Time	Target	Distance	Velocity	Altitude	Relative azimuth angle
${t_0}$	M1	$\left\langle {{\text{0}}{\text{.830,0}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.694,0}}{\text{.186}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.583,0}}{\text{.167}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.171,0}}{\text{.587}}} \right\rangle $
	M2	$\left\langle {{\text{0}}{\text{.603,0}}.227} \right\rangle $	$\left\langle {{\text{0}}{\text{.566,0}}{\text{.314}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.393,0}}{\text{.357}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.061,0}}{\text{.697}}} \right\rangle $
	M3	$\left\langle {{\text{0}}{\text{.667,0}}{\text{.163}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.88,0}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.75,0 }}} \right\rangle $	$\left\langle {{\text{0}}{\text{.758,0}}} \right\rangle $
	M4	$\left\langle {{\text{0}}{\text{.406,0}}{\text{.423}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.442,0}}{\text{.437}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.264,0}}{\text{.486}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.747,0}}{\text{.010}}} \right\rangle $
	M5	$\left\langle {{\text{0}}{\text{.717,0}}{\text{.113}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.655,0}}{\text{.225}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.536,0}}.214} \right\rangle $	$\left\langle {{\text{0}}{\text{.185,0}}{\text{.573}}} \right\rangle $
${t_1}$	M1	$\left\langle {{\text{0}}{\text{.830,0}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.587,0}}{\text{.294}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.75,0}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.110,0}}{\text{.886}}} \right\rangle $
	M2	$\left\langle {{\text{0}}{\text{.541,0}}{\text{.290}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.512,0}}{\text{.360}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.526,0}}{\text{.223}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.053,0}}{\text{.944}}} \right\rangle $
	M3	$\left\langle {{\text{0}}{\text{.481,0}}{\text{.350}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.767,0}}{\text{.113}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.550,0}}{\text{.199}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.053,0}}{\text{.944}}} \right\rangle $
	M4	$\left\langle {{\text{0}}{\text{.413,0}}{\text{.417}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.415,0}}{\text{.465}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.472,0}}{\text{.278}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.318,0}}{\text{.678}}} \right\rangle $
	M5	$\left\langle {{\text{0}}{\text{.583,0}}{\text{.247}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.592,0}}{\text{.288}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.675,0}}{\text{.075}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.113,0}}{\text{.883}}} \right\rangle $
	M6	$\left\langle {{\text{0}}{\text{.432,0}}{\text{.399}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.265,0}}{\text{.615}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.311,0}}{\text{.439}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.061,0}}{\text{.935}}} \right\rangle $
	M7	$\left\langle {{\text{0}}{\text{.359,0}}{\text{.471}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.437,0}}{\text{.443}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.595,0}}{\text{.1}}55} \right\rangle $	$\left\langle {{\text{0}}{\text{.996,0}}} \right\rangle $
	M8	$\left\langle {{\text{0}}{\text{.359,0}}{\text{.471}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.88,0}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.309,0}}{\text{.441}}} \right\rangle $	$\left\langle {{\text{0}}{\text{.981,0}}{\text{.015}}} \right\rangle $

Table 7

Table 8

Fig 4

Table 9

Table 10

Table 11

Table 12

Table 13

Fig 5

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Target	Combat capability	Type	Maneuvering capability	RCS/m²
M1	7.5	Medium(relatively certain)	Relatively high(relatively certain)	0.15
M2	8.5	Very high(very certain)	Medium(relatively certain)	12
M3	12.6	High(relatively certain)	Very high(very certain)	0.08
M4	18.1	High(very certain)	Relatively high(relatively certain)	0.36
M5	9.2	Relatively high(certain)	High(relatively certain)	8
M6	3.1	Low(very certain)	Low(relatively certain)	10
M7	7.5	Very high(very certain)	Medium(very certain)	0.56
M8	11	Very high(very certain)	Relatively low(relatively certain)	0.8

Time	Target	Distance/km	Velocity/Ma	Altitude/m	Relative azimuth angle/(°)
${t_0}$	M1	30	0.96	2000	25.5
	M2	65	0.75	3500	65.5
	M3	60	1.30	1500	3.2
	M4	140	0.65	6000	4.2
	M5	55	0.86	2200	23.2
${t_1}$	M1	35	0.92	2200	45.5
	M2	67	0.79	4000	177.6
	M3	70	1.35	3500	178.5
	M4	135	0.68	5500	14.2
	M5	65	0.94	2500	43.2
	M6	125	0.55	7000	92.5
	M7	80	0.70	3000	2.1
	M8	80	5.50	10000	3.5

Time	Target	${I_1}$	${I_2}$	${I_3}$	${I_4}$	${I_5}$	${I_6}$	${I_7}$	${I_8}$
${t_1}$	M1	0.125	0.331	0.434	0.110	0	0	0	0
	M2	0.075	0	0.127	0.687	0	0	0.111	0
	M3	0.862	0.138	0	0	0	0	0	0
	M4	0.887	0.113	0	0	0	0	0	0
	M5	0.124	0.100	0.137	0.108	0	0	0.531	0
${t_2}$	M1	0.302	0.509	0.081	0.028	0	0	0.08	0
	M2	0	0	0	0.152	0	0	0	0.848
	M3	0	0	0	0	0	0	0	1
	M4	0.740	0.145	0	0	0	0	0	0.115
	M5	0	0	0.197	0.107	0	0	0.62	0.080
	M6	0	0	0	0	0.9	0.1	0	0
	M7	1	0	0	0	0	0	0	0
	M8	1	0	0	0	0	0	0	0

Evaluation language scale	IFS
Evaluation language scale	$ \mu $	$ v $	$ \text{π} $
$ \alpha = 6 $ (Very high)	1	0	0
$ \alpha = 5 $ (High)	0.85	0.10	0.05
$ \alpha = 4 $ (Relatively high)	0.65	0.20	0.15
$ \alpha = 3 $ (Medium)	0.4	0.40	0.20
$ \alpha = 2 $ (Relatively low)	0.2	0.65	0.15
$ \alpha = 1 $ (Low)	0.1	0.85	0.05
$ \alpha = 0 $ (Very low)	0	1	0

Degree of certainty	L	U
Very certain	0.9	1
Relatively certain	0.6	0.9
Certain	0.4	0.6
Relatively uncertain	0.2	0.4
Uncertain	0	0.2